What is your favorite math constant that is NOT a real number?
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ε, the base of the dual numbers.
It’s a nonzero hypercomplex number that squares to zero, enabling automatic differentiation.
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Zero
It's the absence of a number and has all manner of interesting edge cases associated with it.
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{j|∧} or ĵ just a base vector
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ε, the base of the dual numbers.
It’s a nonzero hypercomplex number that squares to zero, enabling automatic differentiation.
Complex numbers
Split-complex numbers Dual numbersAll super rad.
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Zero
It's the absence of a number and has all manner of interesting edge cases associated with it.
Zero is a real number, but interestingly, it's also a pure imaginary number. It's the only number that's both things at once.
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Zero is a real number, but interestingly, it's also a pure imaginary number. It's the only number that's both things at once.
It gets deeper. It's also the same as the 0-k-vector, the 0-k-blade, the 0-multivector, the only number that is its own square besides 1, etc...
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Zero is a real number, but interestingly, it's also a pure imaginary number. It's the only number that's both things at once.
As I said .. lots of edge cases
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Matrix representations in general, if that counts?
Complex numbers, polynomials, the derivative operator, spinors etc. they're all matrices. Numbers are just shorthand labels for certain classes of matrices, fight me.
